Question

Find sin θ if cos θ = 4/7 and θ in quadrant IV. Give an exact answer.

Answer 1

`\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\ -------------------------------\\\\ cos(\theta)=\cfrac{4}{7}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c} \\\\\\ \textit{using the pythagorean theorem to get the opposite side or`

now, the square root gives us both +/- versions, which is it? well, we know the angle θ is in the IV quadrant, well, the sine is "b" is negative there, thus is the negative version then

thus
`\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(\theta)=\cfrac{-√(33)}{7}`